If the rope is moved 1 m outwards, how much longer must it be?
A hard-level "Length" problem.The famous result that the answer does not depend on the original radius. Do not rush to a number — factor out what is common and the reason appears.
GivenA rope goes exactly once round a circular flower bed of radius 10 m / π = 3.14
Hints
- First, the rope as it is: 10 × 2 × 3.14 = 62.8 m.
- Moved outwards, the radius becomes 10 + 1 = 11 m, so the rope is 11 × 2 × 3.14 = 69.08 m.
- The difference is 69.08 − 62.8 = 6.28 m. Do not stop here — look at why it came out like that.
- Written side by side, the 2 and the 3.14 factor out, leaving only 11 − 10 = 1 — just the width of the shift.
- So the answer does not depend on the original size at all. A flower bed of radius 1 m, or the whole Earth — shifting the rope 1 m out always needs just 6.28 m more.
Answer 6.28m
More "Length" problems
- a + b + c = ?
- What is the side of the square?
- How long is MN?
- How long is the rope?
- How long is the pole's shadow?
- How deep was the water?